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| IST1000 | Introduction to Probability | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Zafer KÜÇÜK | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To make students understand the basic concepts of the probability theory: Sample Spaces, Events, Discrete and Continuous sample, Kolmogorov's axioms, the conditional probability of events, independence and Bayes' formula of total probability, Bernoulli scheme, random variables and distribution of random variables. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | understand the basic concepts of probability theory | 2,8 | 1, | | LO - 2 : | construct a mathematical model of stochastic experiment | 2,8 | 1, | | LO - 3 : | have the ability to calculate probability of events | 2,8 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Historical development and subject of the probability theory. Sample space. Events and operations over events. Frequency of event. Definition of the probability in discrete sample space. Classical probability. Algebra and Borel sigma algebra. Definition of the probability in continuous sample space. Kolmogorov's axioms. Probability space. Properties of the probability measure. Geometrical probability. Independence of events. Formula of product of probabilities. Conditional probability. Total probability formula. Bayes's formulas. Sequence of independent trails. Bernoulli scheme. Limit theorems in Bernoulli scheme (Mouavr-Laplace's local and integral formulas, Poisson's theorem, Law of large numbers). Polynomial scheme. Sample Markov chains. Concept of random variable. Operations over random variables. Distribution function and its properties. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Historical development and subject of the probability theory. | | | Week 2 | Sample space. Events and operations over events. | | | Week 3 | Frequency of event.Definition of the probability in discrete sample space. Classical definition and applications of probability. | | | Week 4 | Definitions and applcations of Algebra and Borel sigma algebra. Definition of the probability in continuous sample space. | | | Week 5 | Kolmogorov's axioms. Probability space. Properties of the probability measure. | | | Week 6 | Geometrical probability and its applications. Independence of events, multiplication formula and applications of events. | | | Week 7 | Conditional probability and its applcations. Formula of total probability formula. Bayes's formulas and their applications. | | | Week 8 | Mid-term exam | | | Week 9 | Sequance of independent trails. Bernoulli scheme. | | | Week 10 | Limit theorems in Bernoulli scheme (Mouavr-Laplace's local and integral formulas, Poisson's theorem). | | | Week 11 | Law of large numbers. Bernoulli and Poisson theorems. | | | Week 12 | Polynomial scheme. | | | Week 13 | Simple Markov chains. | | | Week 14 | Concept of random variable (assessbility in comparison to algebra) Operations over random variables. | | | Week 15 | Distribution of variables, distribution functions and its basic properties. | | | Week 16 | End-of-term exam | | | |
| 1 | Akdeniz F. Olasılık ve İstatistik, Ankara Ü., Ankara, 1984, | | | 2 | Nasirova T., Khaniyev T. Yapar C., Ünver İ., Küçük Z. Olasılık. KTÜ Matbaası, Trabzon, 2009. | | | |
| 1 | Kolmogorov A.N. Foundations of the Theory of Probability. New York, 1956. | | | 2 | Ceyhan İnal H., Günay S.Olasılık ve matematiksel istatistik, Ankara,1982. | | | 3 | Ersoy N., Erbaş S.D. Olasılık ve İstatistiğe giriş, Gazi Ü., Ankara, 1992. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 11/04/2019 | 1,5 | 50 | | End-of-term exam | 16 | 04/06/2019 | 1,5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 5 | 4 | 20 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 170 |
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